$\dfrac{ -6g + 6h }{ -2 } = \dfrac{ -2g - 4i }{ -9 }$ Solve for $g$.
Multiply both sides by the left denominator. $\dfrac{ -6g + 6h }{ -{2} } = \dfrac{ -2g - 4i }{ -9 }$ $-{2} \cdot \dfrac{ -6g + 6h }{ -{2} } = -{2} \cdot \dfrac{ -2g - 4i }{ -9 }$ $-6g + 6h = -{2} \cdot \dfrac { -2g - 4i }{ -9 }$ Multiply both sides by the right denominator. $-6g + 6h = -2 \cdot \dfrac{ -2g - 4i }{ -{9} }$ $-{9} \cdot \left( -6g + 6h \right) = -{9} \cdot -2 \cdot \dfrac{ -2g - 4i }{ -{9} }$ $-{9} \cdot \left( -6g + 6h \right) = -2 \cdot \left( -2g - 4i \right)$ Distribute both sides $-{9} \cdot \left( -6g + 6h \right) = -{2} \cdot \left( -2g - 4i \right)$ ${54}g - {54}h = {4}g + {8}i$ Combine $g$ terms on the left. ${54g} - 54h = {4g} + 8i$ ${50g} - 54h = 8i$ Move the $h$ term to the right. $50g - {54h} = 8i$ $50g = 8i + {54h}$ Isolate $g$ by dividing both sides by its coefficient. ${50}g = 8i + 54h$ $g = \dfrac{ 8i + 54h }{ {50} }$ All of these terms are divisible by $2$ $g = \dfrac{ {4}i + {27}h }{ {25} }$